Flexible torque transmission couplings are old and well-known devices for transmitting rotary power under conditions in which misalignment exists between the rotating power source and the machine receiving the rotating power. Flexible couplings employing one or more flex elements consisting of an integral, single piece of material or comprising separate flex elements and other components connected together are widely used. An example of an integral, single element flexible coupling is disclosed in U.S. Pat. No. 3,071,942, issued Jan. 8, 1963. An example of a flexible coupling comprising a number of flex elements and connecting members to provide an overall coupling structure is disclosed in U.S. Pat. No. 2,745,267, issued May 15, 1956. Both types of flexible couplings, however, have the problem of high stress concentrations within the flex elements of the coupling due to transfer of torque from one element of the coupling to another and due to flexure of the elements resulting from misalignment of the coupling. Consequently, torque, speed, and misalignment capabilities are less than would be the case if the stresses could be better distributed throughout the flex elements.